A salvage ship's sonar locates wreckage at a 12 angle of depression. A driver is lowered 40m to the ocean floor. How far does the driver need to walk along the ocean floor to the wreckage? draw a picture
so, did you draw the picture?
40/x = tan 12°
I suspect that the "driver" is really a diver. sheesh.
To answer this question, we can use trigonometry. Here's how to solve it step by step:
1. First, let's draw a diagram to visualize the situation. Draw a horizontal line to represent the ocean floor. Label one end of the line as the starting point for the driver. Draw a vertical line upward from the starting point to represent the location of the wreckage. Label the vertical line as the "wreckage."
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Starting point
2. The problem states that the angle of depression is 12 degrees. An angle of depression is the angle formed by the line of sight downward from an observer to an object below the observer's horizontal level. We can draw this in our diagram. From the starting point, draw a line downward at a 12-degree angle to represent the line of sight to the wreckage.
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Starting point \ Line of sight to wreckage
3. The problem also states that the driver is lowered 40m to the ocean floor. To represent this, draw a horizontal line from the starting point to the driver, parallel to the ocean floor. Label this line as "40m."
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----40m-------\------
Starting point \ Line of sight to wreckage
4. To find the distance the driver needs to walk along the ocean floor to reach the wreckage, let's label this distance as "d." This distance forms the base of a right triangle, with the line of sight to the wreckage being the hypotenuse.
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________\d___\------
Starting point \ Line of sight to wreckage
5. To find the value of "d," we can use trigonometry. We know that the tangent of the angle of depression is equal to the ratio of the opposite side (d) to the adjacent side (40m).
tan(12 degrees) = d / 40m
6. Rearranging the equation, we have:
d = 40m * tan(12 degrees)
7. Now you can use a scientific calculator to evaluate the tangent of 12 degrees and then multiply it by 40m to find the value of "d".
d ≈ 8.48 meters
Therefore, the driver needs to walk approximately 8.48 meters along the ocean floor to reach the wreckage.